Marko, thank you for this very good analysis!
I was thinking a lot about this problem and came pretty much to the same conclusion but without a good foundation on DOF.
This bothered me a lot and I was quite disappointed in my camera limits (there were other attempts besides this picture). Now you confirmed that I didn't screw up too much (I could have been shooting at 24mm).
Basically the task I've set is beyond technical capabilities available to me. The only thing I can think of is may be a Lightroom capability to remove noise if I go to a higher ISO (but again it makes pixels bigger an my sharpness is lost to lower resolution even if all noise is removed).
So I guess this kind of task would be for Nikon D800 or Hasselblad with 40 Mpx :-)
Once again thank you for reassuring me!
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